Problem: Solve for $q$. $3\left(q+\dfrac43\right) = 2$
Answer: Let's divide and then subtract to get $q$ by itself. $\begin{aligned}3\left(q+\dfrac43\right) &= 2 \\ \\\\ \dfrac{3\left(q+\dfrac43\right)}{{3}} &= \dfrac{2}{{3}} ~~~~~~~\text{divide each side by } {3}\\ \\ \dfrac{\cancel{3}\left(q+\dfrac43\right)}{\cancel{{3}}} &= \dfrac{2}{{3}} \\ \\ q +\dfrac43&= \dfrac{2}{{3}} \end{aligned}$ $\begin{aligned} \\ q+\dfrac43 {-\dfrac43}&= \dfrac23{-\dfrac43}~~~~{\text{subtract }\dfrac43} \text{ from each side} \text{ to get } q \text{ by itself }\\ \\ q+\cancel{ \dfrac43} {{-}\cancel{{\dfrac43}}}&= \dfrac23{-\dfrac43}\\ \\ q &=\dfrac23{-\dfrac43}\end{aligned}$ The answer: $q={-\dfrac23}$ Let's check to make sure. $\begin{aligned} 3\left(q+\dfrac43\right) &= 2 \\\\ 3\left({-\dfrac23}+\dfrac43\right) &\stackrel{?}{=} 2 \\\\ 3\left(\dfrac23\right)&\stackrel{?}{=} 2 \\\\ 2 &= 2 ~~~~~~~~~~\text{Yes!} \end{aligned}$